Difference between Charge–Voltage Relations of Ordinary and Fractional Capacitors

In an ordinary time-varying capacitor, there is debate on whether a time-domain multiplication or a time-domain convolution of capacitance and voltage determines charge. The objective of this work is to resolve this question by experiments on a time-varying capacitor in parallel with a resistor. It was implemented by a motor-driven potentiometer and op-amps. The response matched a power-law function over about two decades of time, and not an exponential, for several sets of parameters. This confirms the time-domain multiplication model. This result is the opposite of that obtained for a constant phase element (CPE) in its common time- and frequency-varying capacitor interpretation. This demonstrates that a CPE is fundamentally different from an ordinary time- and frequency-varying capacitor.